Memory
Hakim Weatherspoon
CS 3410, Spring 2013
Computer Science
Cornell University
Big Picture: Building a Processor
memory
+4
inst
register
file
+4
=?
PC
control
offset
new
pc
alu
cmp
target
imm
extend
A Single cycle processor
addr
din
dout
memory
Goals for today
Review
• Finite State Machines
Memory
•
•
•
•
Register Files
Tri-state devices
SRAM (Static RAM—random access memory)
DRAM (Dynamic RAM)
Which statement(s) is true
(A) In a Moore Machine output depends on both
current state and input
(B) In a Mealy Machine output depends on current
state and input
(C) In a Mealy Machine output depends on next
state and input
(D) All the above are true
(E) None are true
Mealy Machine
Registers
General Case: Mealy Machine
Current
State
Input
Comb.
Logic
Output
Next State
Outputs and next state depend on both
current state and input
Moore Machine
Registers
Special Case: Moore Machine
Current
State
Comb.
Logic
Output
Input
Comb.
Logic
Next State
Outputs depend only on current state
Example #2: Digital Door Lock
Digital Door Lock
Inputs:
• keycodes from keypad
• clock
Outputs:
• “unlock” signal
• display how many keys pressed so far
Door Lock: Inputs
Assumptions:
• signals are synchronized to clock
• Password is B-A-B
K
A
B
K A B Meaning
0 0 0 Ø (no key)
1 1 0 ‘A’ pressed
1 0 1 ‘B’ pressed
Door Lock: Outputs
Assumptions:
• High pulse on U unlocks door
D3D2D1D0
4 LED 8
dec
U
Strategy:
(1) Draw a state diagram (e.g. Moore Machine)
(2) Write output and next-state tables
(3) Encode states, inputs, and outputs as bits
(4) Determine logic equations for next state and outputs
Door Lock: Simplified State Diagram
Ø
Ø
G1
”1”
“A”
“B”
G2
”2”
else
“B”
else
G3
”3”, U
any
Idle
”0”
Ø
else
any
B1
”1”
else B2
”2”
Ø
else
B3
”3”
Ø
(1) Draw a state diagram (e.g. Moore Machine)
Door Lock: Simplified State Diagram
Ø
Ø
G1
”1”
“A”
else
“B”
G2
”2”
else
“B”
G3
”3”, U
any
Idle
”0”
Ø
else
else
B1
”1”
else B2
”2”
Ø
Ø
(1) Draw a state diagram (e.g. Moore Machine)
Door Lock: Simplified State Diagram
Ø
Ø
G1
”1”
“A”
else
“B”
G2
”2”
else
“B”
Cur.
State
Idle
”0”
Ø
else
else
B1
”1”
else B2
”2”
Ø
Ø
(2) Write output and next-state tables
G3
”3”, U
any
Output
Door Lock: Simplified State Diagram
Ø
Ø
G1
”1”
“A”
else
“B”
G2
”2”
else
Idle
”0”
Ø
else
else
B1
”1”
else B2
”2”
Ø
Ø
“B”
Cur.
State
Idle
G1
G2
G3
B1
B2
(2) Write output and next-state tables
G3
”3”, U
any
Output
“0”
“1”
“2”
“3”, U
“1”
“2”
Door Lock: Simplified State Diagram
Ø
Cur. State
Ø
G1
”1”
“A”
else
“B”
G2
”2”
“B”
else
Idle
”0”
Ø
else
else
B1
”1”
else B2
”2”
Ø
Ø
(2) Write output and next-state tables
Input
Next State
G3
”3”, U
any
Door Lock: Simplified State Diagram
Ø
G1
”1”
“A”
else
“B”
Idle
”0”
Ø
else
else
B1
”1”
else
Cur. State
Ø
Idle
G2 Idle “B”
”2”Idle
elseG1
G1
G1
G2
G2
G2
G3
B2 B1
”2” B1
B2
Ø
B2
Ø
(2) Write output and next-state tables
Input
Next State
Ø
Idle
“B”G3
G1
”3”, U
“A”
B1
Ø
any G1
“A”
G2
“B”
B2
Ø
B2
“B”
G3
“A”
Idle
any
Idle
Ø
B1
K
B2
Ø
B2
K
Idle
State Table Encoding
SCur.
SState
S0
2
1
0 Idle
0 0
0 G1
0 1
0 G2
1 0
0 G3
1 1
1 B1
0 0
1 B2
0 1
D3
0
0
0
0
0
0
DOutput
2 D1 D0
0 “0”
0 0
0 “1”
0 1
0 “2”
1 0
0“3”,
1 U1
0 “1”
0 1
0 “2”
1 0
U
0
0
0
1
0
0
Cur.
S2 SState
1 S0
0 Idle
0 0
0 Idle
0 0
0 Idle
0 0
0 G1
0 1
0 G1
0 1
0 G1
0 1
0 G2
1 0
0 G2
1 0
0 G2
1 0
0 G3
1 1
1 B1
0 0
1 B1
0 0
1 B2
0 1
1 B2
0 1
K Input
A
B
0
Ø
0
0
1 “B”
0
1
1 “A”
1
0
0
Ø
0
0
1 “A”
1
0
1 “B”
0
1
0
Ø
0
0
1 “B”
0
1
1 “A”
1
0
x any
x
x
0
Ø
0
0
1
K
x
x
0
Ø
0
0
1
K
x
x
State
S2 S 1 8 S0
4 Meaning
K
A
B
D3D2D1D0
dec 0 0
Idle
0
0 0 0 Ø (no key)
U 0 0 1
G1
1 1 0 ‘A’ pressed
K 0
G2
0
1
1 0 1 ‘B’ pressed
A
G3
0 1 1
B
B1
1 0 0
(3) Encode
states,
and outputs as bits
B2
1 0 inputs,
1
S’
Next
2 S’State
1 S’0
0 Idle
0 0
0 G1
0 1
1 B1
0 0
0 G1
0 1
0 G2
1 0
1 B2
0 1
0 B2
1 0
0 G3
1 1
0 Idle
0 0
0 Idle
0 0
1 B1
0 0
1 B2
0 1
1 B2
0 1
0 Idle
0 0
3bit
Reg
S2-0
D3-0
4
dec
Door Lock: Implementation
U
clk
S2-0
K
A
S’2-0
B
U = S2S1S0
D0 = S2S1S0 + S2S1S0 + S2 S1S0
D1 = S2S1S0 + S2S1S0 + S2S1S0
S2
0
0
0
0
1
1
S1
0
0
1
1
0
0
S0
0
1
0
1
0
1
D3
0
0
0
0
0
0
D2
0
0
0
0
0
0
D1
0
0
1
1
0
1
D0
0
1
0
1
1
0
(4) Determine logic equations for next state and outputs
U
0
0
0
1
0
0
Door Lock: Implementation
3bit
Reg
clk
S2-0
K
A
B
K
0
1
1
0
1
1
0
1
1
x
0
1
0
1
dec
S2-0
S2 S1 S0
4
D03-00 0
0 0 0
U
0 0 0
0 0 1
0 0 1
0 0 1
0S’2-0
1 0
0 1 0
0 1 0
0 1 1
1 0 0
1 0 0
1 0 1
1 0 1
A
0
0
1
0
1
0
0
0
1
x
0
x
0
x
B
0
1
0
0
0
1
0
1
0
x
0
x
0
x
S’2 S’1 S’0
0 0 0
0 0 1
1 0 0
0 0 1
0 1 0
1 0 1
0 1 0
0 1 1
0 0 0
0 0 0
1 0 0
1 0 1
1 0 1
0 0 0
S0’ = ?
S1’ = ?
S2’ = S2S1S0KAB + S2S1S0KAB + S2S1S2KAB + S2S1S0K + S2 S1S0 KAB
3bit
Reg
S2-0
D3-0
4
dec
Door Lock: Implementation
U
clk
S2-0
K
A
S’2-0
B
Strategy:
(1) Draw a state diagram (e.g. Moore Machine)
(2) Write output and next-state tables
(3) Encode states, inputs, and outputs as bits
(4) Determine logic equations for next state and outputs
Administrivia
Make sure to go to your Lab Section this week
•
•
•
•
•
Find project partners this week (for upcoming project1 next week)
Lab2 due in class this week (it is not homework)
Design Doc for Lab1 due yesterday, Monday, Feb 4th
Completed Lab1 due next week, Monday, Feb 11th
Work alone
Homework1 is due Wednesday
• Work alone
• Academic Integrity
BUT, use your resources
• Lab Section, Piazza.com, Office Hours, Homework Help Session,
• Class notes, book, Sections, CSUGLab
Second C Primer: Thursday, B14 Hollister, 6-8pm
Administrivia
Check online syllabus/schedule
• http://www.cs.cornell.edu/Courses/CS3410/2013sp/schedule.html
Slides and Reading for lectures
Office Hours
Homework and Programming Assignments
Prelims (in evenings):
• Tuesday, February 26th
• Thursday, March 28th
• Thursday, April 25th
Schedule is subject to change
Collaboration, Late, Re-grading Policies
“Black Board” Collaboration Policy
• Can discuss approach together on a “black board”
• Leave and write up solution independently
• Do not copy solutions
Late Policy
• Each person has a total of four “slip days”
• Max of two slip days for any individual assignment
• Slip days deducted first for any late assignment,
cannot selectively apply slip days
• For projects, slip days are deducted from all partners
• 25% deducted per day late after slip days are exhausted
Regrade policy
• Submit written request to lead TA,
and lead TA will pick a different grader
• Submit another written request,
lead TA will regrade directly
• Submit yet another written request for professor to regrade.
Lab1: Thoughts thus far
Great experience!
But, read all instructions (multiple times)!
Sign up for design doc meetings early
• We were very lenient for Lab1
• In future, CMS will lock the Friday after release
• lose points for not signing up before lock, canceling last minute,
and/or not showing up
Design doc meeting
• Not the same as office hours
You are presenting your current design during design doc meeting
• Bring printout of your design document
• TA will grade and give feedback based on your presentation of your
design
Goals for today
Memory
•
•
•
•
CPU: Register Files (i.e. Memory w/in the CPU)
Scaling Memory: Tri-state devices
Cache: SRAM (Static RAM—random access memory)
Memory: DRAM (Dynamic RAM)
Goal:
How do we store results from ALU computations?
How do we use stored results in subsequent
operations?
Register File
How does a Register File work? How do we design it?
Big Picture: Building a Processor
memory
+4
inst
register
file
+4
=?
PC
control
offset
new
pc
alu
cmp
target
imm
extend
A Single cycle processor
addr
din
dout
memory
Register File
Register File
• N read/write registers
• Indexed by
register number
32
DW Dual-Read-Port
QA
Single-Write-Port Q
B
32 x 32
Register File
W
1
RW RA RB
5
5
5
32
32
Register File
D0
D1
D2
Recall: Register
•D flip-flops in parallel
•shared clock
•extra clocked inputs:
write_enable, reset, …
D3
4
clk
4-bit
reg 4
clk
Register File
Register File
32
D
• N read/write registers
• Indexed by
register number
Reg 0
Reg 1
5-to-32
decoder
5
….
Reg 30
Reg 31
RW W
How to write to one register in the register file?
• Need a decoder
Activity# write truth table for 3-to-8 decoder
Register File
32
D
• N read/write registers
• Indexed by
register number
Reg 0
Reg 1
5-to-32
decoder
5
….
Reg 30
Reg 31
RW W
How to write to one register in the register file?
• Need a decoder
Register File
Register File
• N read/write registers
• Indexed by
register number
Reg 0
Reg 1
….
32
….
Reg 30
Reg 31
….
M
U
X
M
U
X
How to read from two registers?
• Need a multiplexor
5
RA
5
RB
32
QA
32
QB
Register File
Register File
32
D
• N read/write registers
• Indexed by
register number
Reg 0
Reg 1
5-to-32
decoder
….
….
Reg 30
Reg 31
Implementation:
• D flip flops to store bits
• Decoder for each write port
• Mux for each read port
32
….
5
5
W RW RA
M
U
X
M
U
X
5
RB
32
QA
32
QB
Register File
Register File
• N read/write registers
• Indexed by
register number
32
DW Dual-Read-Port
Implementation:
• D flip flops to store bits
• Decoder for each write port
• Mux for each read port
QA
Single-Write-Port Q
B
32 x 32
Register File
W
1
RW RA RB
5
5
5
32
32
Register File
Register File
What happens if same
• N read/write registers register read and written
• Indexed by
during same clock cycle?
register number
Implementation:
• D flip flops to store bits
• Decoder for each write port
• Mux for each read port
Tradeoffs
Register File tradeoffs
8-to-1 mux
a
+ Very fast (a few gate delays for b
both read and write)
c
+ Adding extra ports is
d
straightforward
e
– Doesn’t scale
f
e.g. 32MB register file with
g
32 bit registers
Need 32x 1M-to-1 multiplexor h
and 32x 10-to-1M decoder
How many logic gates/transistors?
s2s1s0
Takeway
Register files are very fast storage (only a few gate
delays), but does not scale to large memory sizes.
Goals for today
Memory
•
•
•
•
CPU: Register Files (i.e. Memory w/in the CPU)
Scaling Memory: Tri-state devices
Cache: SRAM (Static RAM—random access memory)
Memory: DRAM (Dynamic RAM)
Next Goal
How do we scale/build larger memories?
Building Large Memories
Need a shared bus (or shared bit line)
• Many FlipFlops/outputs/etc. connected to single wire
• Only one output drives the bus at a time
D0 S0
D1 S1
D2 S2
D3 S3
D1023 S1023
shared line
• How do we build such a device?
Tri-State Devices
Tri-State Buffers
• If enabled (E=1), then Q = D
• Otherwise, Q is not connected (z = high impedance)
E
D
Q
E
0
0
1
1
D Q
0 z
1 z
0 0
1 1
Activity#2: Tri-State Buffer from an Inverter
Tri-State Buffers
• If enabled (E=1), then Q = D
• Otherwise, Q is not connected (z = high impedance)
E
Vsupply
D
Q
E
0
0
1
1
D Q
0 z
1 z
0 0
1 1
D
Q
Gnd
Tri-State Devices
Tri-State Buffers
• If enabled (E=1), then Q = D
• Otherwise, Q is not connected (z = high impedance)
E
D
E
Q
D
E
0
0
1
1
D Q
0 z
1 z
0 0
1 1
Vsupply
D
Q
Gnd
Tri-State Devices
Tri-State Buffers
• If enabled (E=1), then Q = D
• Otherwise, Q is not connected (z = high impedance)
E
D
Vsupply
E
Q
0
1
D
E
0
0
1
1
D Q
0 z
1 z
0 0
1 1
0
off
0
A
B
AND NAND
A B OR NOR
0
0
0
1
0 0 0
1
0
1
0
1
0 1 1
0
1
0
0
1
1 0 1
0
1
1
1
0
1 1 1
0
off
Gnd
Q
z
Tri-State Devices
Tri-State Buffers
• If enabled (E=1), then Q = D
• Otherwise, Q is not connected (z = high impedance)
E
D
E
Q
1
D
E
0
0
1
1
D Q
0 z
1 z
0 0
1 1
Vsupply
0
1
0
1
off
1
on
0
A
B
AND NAND
A B OR NOR
0
0
0
1
0 0 0
1
0
1
0
1
0 1 1
0
1
0
0
1
1 0 1
0
1
1
1
0
1 1 1
0
Gnd
Q
0
Tri-State Devices
Tri-State Buffers
• If enabled (E=1), then Q = D
• Otherwise, Q is not connected (z = high impedance)
E
D
E
Q
1
D
E
0
0
1
1
D Q
0 z
1 z
0 0
1 1
Vsupply
1
0
1
1
on
0
off
1
A
B
AND NAND
A B OR NOR
0
0
0
1
0 0 0
1
0
1
0
1
0 1 1
0
1
0
0
1
1 0 1
0
1
1
1
0
1 1 1
0
Gnd
Q
1
Shared Bus
D0 S0
D1 S1
D2 S2
D3 S3
D1023 S1023
shared line
Takeway
Register files are very fast storage (only a few gate
delays), but does not scale to large memory sizes.
Tri-state Buffers allow scaling since multiple
registers can be connected to a single output, while
only one register actually drives the output.
Goals for today
Memory
•
•
•
•
CPU: Register Files (i.e. Memory w/in the CPU)
Scaling Memory: Tri-state devices
Cache: SRAM (Static RAM—random access memory)
Memory: DRAM (Dynamic RAM)
Next Goal
How do we build large memories?
Use similar designs as Tri-state Buffers to connect
multiple registers to output line. Only one register
will drive output line.
SRAM
Static RAM (SRAM)—Static Random Access Memory
Decoder
Address
• Essentially just D-Latches plus Tri-State Buffers
• A decoder selects which line of memory to access
Data
(i.e. word line)
• A R/W selector determines the
type of access
• That line is then coupled to
the data lines
SRAM
Static RAM (SRAM)—Static Random Access Memory
• Essentially just D-Latches plus Tri-State Buffers
• A decoder selects which line of memory to access
(i.e. word line)
• A R/W selector determines the 22
Address
type of access
• That line is then coupled to
SRAM
8
8
4M
x
8
the data lines
Din
Dout
Chip Select
Write Enable
Output Enable
SRAM
Din[1]
E.g. How do we design
a 4 x 2 SRAM Module?
Din[2]
D Q
D Q
enable
enable
D Q
D Q
enable
enable
0
(i.e. 4 word lines that are
each 2 bits wide)?
Address
2-to-4
decoder
1
2
D Q
4 x 2 SRAM
D Q
enable
enable
D Q
D Q
enable
enable
2
3
Write Enable
Output Enable
Dout[1]
Dout[2]
SRAM
Din[1]
E.g. How do we design
a 4 x 2 SRAM Module?
Din[2]
D Q
D Q
enable
enable
D Q
D Q
enable
enable
D Q
D Q
enable
enable
D Q
D Q
enable
enable
0
(i.e. 4 word lines that are
each 2 bits wide)?
Address
2-to-4
decoder
1
2
2
3
Write Enable
Output Enable
Dout[1]
Dout[2]
SRAM
Bit line
Din[1]
Word line
E.g. How do we design
a 4 x 2 SRAM Module?
Din[2]
D Q
D Q
enable
enable
D Q
D Q
enable
enable
D Q
D Q
enable
enable
D Q
D Q
enable
enable
0
(i.e. 4 word lines that are
each 2 bits wide)?
Address
2-to-4
decoder
1
2
2
3
Write Enable
Output Enable
Dout[1]
Dout[2]
Typical SRAM Cell
B
Pass-Through
Transistors
bit line
SRAM Cell
B
word line
Each cell stores one bit, and requires 4 – 8 transistors (6 is typical)
Typical SRAM Cell
2)
Enable(wordline
(wordline==0)
1)
Disabled
1
1) Pre-charge
B = Vsupply/2
3) Cell pulls B high
i.e. B = 1
on
off
B
bit line
SRAM Cell
word line
0
on
off
1) Pre-charge
B = Vsupply/2
3) Cell pulls B low
i.e. B = 0
B
Each cell stores one bit, and requires 4 – 8 transistors (6 is typical)
Read:
• pre-charge B and B to Vsupply/2
• pull word line high
• cell pulls B or B low, sense amp detects voltage difference
Typical SRAM Cell
1)
Enable(wordline
(wordline==0)
1)
Disabled
1→0
on
off
2) Drive B low
i.e. B = 0
B
bit line
SRAM Cell
word line
0 →1
on
off
2) Drive B high
i.e. B = 1
B
Each cell stores one bit, and requires 4 – 8 transistors (6 is typical)
Read:
• pre-charge B and B to Vsupply/2
• pull word line high
• cell pulls B or B low, sense amp detects voltage difference
Write:
• pull word line high
• drive B and B to flip cell
SRAM
Bit line
Din[1]
Word line
E.g. How do we design
a 4 x 2 SRAM Module?
Din[2]
D Q
D Q
enable
enable
D Q
D Q
enable
enable
D Q
D Q
enable
enable
D Q
D Q
enable
enable
0
(i.e. 4 word lines that are
each 2 bits wide)?
Address
2-to-4
decoder
1
2
2
3
Write Enable
Output Enable
Dout[1]
Dout[2]
SRAM
Din[1]
E.g. How do we design
a 4 x 2 SRAM Module?
Din[2]
D Q
D Q
enable
enable
D Q
D Q
enable
enable
0
(i.e. 4 word lines that are
each 2 bits wide)?
Address
2-to-4
decoder
1
2
D Q
4 x 2 SRAM
D Q
enable
enable
D Q
D Q
enable
enable
2
3
Write Enable
Output Enable
Dout[1]
Dout[2]
SRAM
Din
E.g. How do we design
a 4M x 8 SRAM Module?
8
(i.e. 4M word lines that
are each 8 bits wide)?
22
Address
4M x 8 SRAM
Chip Select
Write Enable
Output Enable
Dout
8
SRAM
E.g. How do we design
a 4M x 8 SRAM Module?
4M x 8 SRAM
Address [21-10]
Address [9-0]
12
10
12 x
4096
decoder
4k x 4k x 4k x 4k x 4k x 4k x 4k x 4k x
1024 1024 1024 1024 1024 1024 1024 1024
SRAM SRAMSRAM SRAMSRAM SRAMSRAM SRAM
1024
1024 1024
mux mux mux
1
1
1
1024 1024
1024 1024
1024
mux mux mux mux
mux
1
1
1
1
1
Dout[7]Dout[6] Dout[5]Dout[4] Dout[3]Dout[2] Dout[1]Dout[0]
SRAM
E.g. How do we design
a 4M x 8 SRAM Module?
4M x 8 SRAM
Row
decoder
Address [21-10]
Address [9-0]
12
10
Chip Select (CS)
R/W Enable
4k x 4k x 4k x 4k x 4k x 4k x 4k x 4k x
1024 1024 1024 1024 1024 1024 1024 1024
SRAM SRAMSRAM SRAMSRAM SRAMSRAM SRAM
1024
1024 1024
1024 1024
1024 1024
column selector, sense amp, and I/O circuits
8
Shared Data Bus
1024
SRAM Modules and Arrays
4M x 8
SRAM
4M x 8
SRAM
4M x 8
SRAM
4M x 8
SRAM
R/W
A21-0
CS
msb
lsb
Bank 2
CS
Bank 3
CS
Bank 4
CS
SRAM Summary
SRAM
•A few transistors (~6) per cell
•Used for working memory (caches)
•But for even higher density…
Dynamic-RAM (DRAM)
• Data values require constant refresh
bit line
Dynamic RAM: DRAM
Capacitor
Gnd
Each cell stores one bit, and requires 1 transistors
word line
Dynamic-RAM (DRAM)
Pass-Through
Transistors
• Data values require constant refresh
bit line
Dynamic RAM: DRAM
Capacitor
Gnd
Each cell stores one bit, and requires 1 transistors
word line
Dynamic-RAM (DRAM)
Disabled
2) Enable(wordline
(wordline==0)
1)
0
Capacitor
off
on
bit line
Dynamic RAM: DRAM
word line
1) Pre-charge
B = Vsupply/2
3) Cell pulls B low
i.e. B = 0
Gnd
Each cell stores one bit, and requires 1 transistors
Read:
• pre-charge B and B to Vsupply/2
• pull word line high
• cell pulls B low, sense amp detects voltage difference
Dynamic-RAM (DRAM)
Disabled
1) Enable(wordline
(wordline==0)
1)
bit line
Dynamic RAM: DRAM
word line
0 →1
Capacitor
Gnd
on
off
2) Drive B high
i.e. B = 1
Charges capacitor
Each cell stores one bit, and requires 4 – 8 transistors (6 is typical)
Read:
• pre-charge B and B to Vsupply/2
• pull word line high
• cell pulls B or B low, sense amp detects voltage difference
Write:
• pull word line high
• drive B charges capacitor
DRAM vs. SRAM
Single transistor vs. many gates
• Denser, cheaper ($30/1GB vs. $30/2MB)
• But more complicated, and has analog sensing
Also needs refresh
•
•
•
•
Read and write back…
…every few milliseconds
Organized in 2D grid, so can do rows at a time
Chip can do refresh internally
Hence… slower and energy inefficient
Memory
Register File tradeoffs
+
+
–
–
Very fast (a few gate delays for both read and write)
Adding extra ports is straightforward
Expensive, doesn’t scale
Volatile
Volatile Memory alternatives: SRAM, DRAM, …
– Slower
+ Cheaper, and scales well
– Volatile
Non-Volatile Memory (NV-RAM): Flash, EEPROM, …
+ Scales well
– Limited lifetime; degrades after 100000 to 1M writes
Summary
We now have enough building blocks to build
machines that can perform non-trivial
computational tasks
Register File: Tens of words of working memory
SRAM: Millions of words of working memory
DRAM: Billions of words of working memory
NVRAM: long term storage
(usb fob, solid state disks, BIOS, …)
Next time we will build a simple processor!